Experiments in Fluids

, 59:31 | Cite as

Three-dimensional particle tracking velocimetry algorithm based on tetrahedron vote

  • Yutong Cui
  • Yang Zhang
  • Pan Jia
  • Yuan Wang
  • Jingcong Huang
  • Junlei Cui
  • Wing T. Lai
Research Article


A particle tracking velocimetry algorithm based on tetrahedron vote, which is named TV-PTV, is proposed to overcome the limited selection problem of effective algorithms for 3D flow visualisation. In this new cluster-matching algorithm, tetrahedrons produced by the Delaunay tessellation are used as the basic units for inter-frame matching, which results in a simple algorithmic structure of only two independent preset parameters. Test results obtained using the synthetic test image data from the Visualisation Society of Japan show that TV-PTV presents accuracy comparable to that of the classical algorithm based on new relaxation method (NRX). Compared with NRX, TV-PTV possesses a smaller number of loops in programming and thus a shorter computing time, especially for large particle displacements and high particle concentration. TV-PTV is confirmed practically effective using an actual 3D wake flow.

List of symbols


A, B, C, D, E, F

Parameters in NRX


Angle characteristic parameter of tetrahedron


Characteristic matrix of tetrahedron


Difference between reference tetrahedrons i and j


Maximum inter-frame particle displacement


Set of reference tetrahedrons of n


Set of reference tetrahedrons of m


Reference tetrahedron of n


Reference tetrahedron of m


Edge characteristic parameter of tetrahedron


Candidate particle for n in the second frame


Particle in the first frame


Number of reference tetrahedrons of n


Number of reference tetrahedrons of m


Number of candidates for n


Number of particles in the first frame


Number of reference particles of n (in NRX)


Number of candidates for a reference particle of n (in NRX)


Number of iteration loops for NRX


Number of correctly matched particle pairs by PTV


Number of correctly missed particles by PTV


Total number of loops in the programming of NRX


Total number of loops in the programming of TV-PTV


Origin in the Cartesian coordinate system


Vertex of tetrahedron


Radius of the inscribed sphere of the cubic flow field


Interrogation radius to enclose reference particles (in NRX)


Interrogation radius to enclose candidate particles


Total number of votes that m receives from n


Number of votes that m receives from i


Average vote rate of tetrahedrons


Coordinate vector of particle


Stream-wise dimension


Span-wise dimension


Vertical dimension

Greek characters


Tetrahedron difference parameter


Tetrahedron vote parameter


Error rate of PTV


Accuracy of PTV



This work is funded by National Natural Science Foundation of China (11402190) and China Postdoctoral Science Foundation (2014M552443). Pan Jia is supported by the project LabEx PALM PoPS.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yutong Cui
    • 1
  • Yang Zhang
    • 1
  • Pan Jia
    • 2
  • Yuan Wang
    • 1
  • Jingcong Huang
    • 1
  • Junlei Cui
    • 3
  • Wing T. Lai
    • 3
  1. 1.Department of Fluid Machinery and EngineeringXi’an Jiaotong UniversityXi’anChina
  2. 2.Laboratoire de Physique des Solides (LPS, UMR 8502)CNRS, Univ. Paris-Sud, Univ. Paris-SaclayOrsayFrance
  3. 3.TSI IncorporatedShoreviewUSA

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